python3 << "EOF"
import itertools
M=[[[1,2,0,1],[0,1,2,1],[2,0,1,1],[1,1,0,2]],[[2,0,1,1],[1,2,1,0],[0,1,2,1],[1,0,1,2]],[[1,1,2,0],[2,1,0,1],[1,0,1,2],[0,2,1,1]],[[0,2,1,1],[1,0,2,1],[2,1,0,1],[1,1,2,0]]]
C=[]
for q in itertools.product(range(4),repeat=6):
 c=(0,)+q
 if any((c[i]+2*c[i+1])%5==1 for i in range(1,6)):continue
 if (2*c[1]+c[3]+c[5]+c[6])%5!=4:continue
 if (c[2]+2*c[4]+c[6])%4!=1:continue
 if sum(c[i]==0 for i in range(1,7))%2!=0:continue
 if c[1]==c[5]:continue
 if c[3]+c[6]<2:continue
 C.append(c)
C.sort(key=lambda c:(c[6],c[2],c[4],c[1],c[5],c[3]))
print("N",len(C))
S=[33,8,57,14]
for t,c in enumerate(C,1):
 A=sum(i*c[i] for i in range(1,7))
 B=sum(c[i]>c[i+1] for i in range(1,6))
 Ct=sum((c[i]+1)*(c[7-i]+2) for i in range(1,4))
 Dt=c[1]*c[4]+2*c[2]*c[5]+3*c[3]*c[6]
 m=(A+2*B+Ct+Dt+t)%4
 r=(c[1]+2*c[2]+c[3]+3*c[4]+c[5]+2*c[6]+t)%3
 u=[A+B+t,Ct+2*t,Dt+A+3*t,B+Ct+Dt]
 T=[]
 for i in range(4):
  val=u[i]
  for j in range(4):
   val=val+M[m][i][j]*S[j]
  T.append(val%97)
 S=T
 if r==0:
  S=[(S[i]+[2,0,3,1][i])%97 for i in range(4)]
 elif r==1:
  S=[(S[i]-[1,4,0,2][i])%97 for i in range(4)]
 else:
  S=[S[2]%97,S[0]%97,S[3]%97,S[1]%97]
 print(t,c[1:],A,B,Ct,Dt,m,r,u,S)
print("FINAL",S)
EOF